Monte Carlo Study of the abBA Experiment: Detector Response and Physics Analysis

The abBA collaboration proposes to conduct a comprehensive program of precise measurements of neutron $\beta$-decay coefficients $a$ (the correlation between the neutrino momentum and the decay electron momentum), $b$ (the electron energy spectral distortion term), $A$ (the correlation between the neutron spin and the decay electron momentum), and $B$ (the correlation between the neutron spin and the decay neutrino momentum) at a cold neutron beam facility. We have used a GEANT4-based code to simulate the propagation of decay electrons and protons in the electromagnetic spectrometer and study the energy and timing response of a pair of Silicon detectors. We used these results to examine systematic effects and find the uncertainties with which the physics parameters $a$, $b$, $A$, and $B$ can be extracted from an over-determined experimental data set.